exam Maths Puzzle Numerical Ability

How do you interpret the solution of a system of equations by the corresponding graph?

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I HAVE A QUESTION ON SOLVING BY FACTORING((( X^2+6X+8=0 ))) please help me solve this
a.calculate the value of the discriminant of x^2+x+3=0
b.by examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x^2+x+3 have?why?
this is under 1 problem. thank you tutor.